Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 6930.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6930.v1 | 6930s1 | \([1, -1, 1, -233, 1321]\) | \(51603494067/4336640\) | \(117089280\) | \([2]\) | \(2560\) | \(0.28997\) | \(\Gamma_0(N)\)-optimal |
6930.v2 | 6930s2 | \([1, -1, 1, 247, 5737]\) | \(61958108493/573927200\) | \(-15496034400\) | \([2]\) | \(5120\) | \(0.63655\) |
Rank
sage: E.rank()
The elliptic curves in class 6930.v have rank \(1\).
Complex multiplication
The elliptic curves in class 6930.v do not have complex multiplication.Modular form 6930.2.a.v
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.